Let's modify the logistic differential equation of this example as follows: OP -0.050 (1-1000)- (a) Suppose P(1) represents a fish population at time t, where t is measured in weeks. Explain the meaning of the final term in the equation (-12). The term -12 represents a harvesting of fish at a constant ✔rate-in this case, 12 [lish/week✔✔✔ This is the rate at which fish are caught (b) Draw a direction field for this differential equation. Use the direction field to sketch several solution curves. P 1200) E P 1000! ● 800 600k P = 450 400 200 of 0 P 1200 1000 800 600 12 1 400 ***L 50 100 150 200 250 300 350 For P600, P(t)-Select-- For Po> 600, P(t)-Select- v V V 1500 v 1000 Describe what happens to the fish population for various initial populations. For 0 < P < 400, P(t) -Select--- For P 400, P(t)-Select-- For 400 < P < 600, P(t)-Select-- O Graph the solutions and compare with your sketches in part (b). P 500 (c) What are the equilibrium solutions? (Enter your answers as a comma-separated list.) Pa 1300 044 flip 0 50 100 150 200 250 300 350 P 1000 ***** .. 500 (d) Solve this differential equation explicitly, either by using partial fractions or with a computer algebra system. Use the initial populations 350 and 4 P-350 " P
Let's modify the logistic differential equation of this example as follows: OP -0.050 (1-1000)- (a) Suppose P(1) represents a fish population at time t, where t is measured in weeks. Explain the meaning of the final term in the equation (-12). The term -12 represents a harvesting of fish at a constant ✔rate-in this case, 12 [lish/week✔✔✔ This is the rate at which fish are caught (b) Draw a direction field for this differential equation. Use the direction field to sketch several solution curves. P 1200) E P 1000! ● 800 600k P = 450 400 200 of 0 P 1200 1000 800 600 12 1 400 ***L 50 100 150 200 250 300 350 For P600, P(t)-Select-- For Po> 600, P(t)-Select- v V V 1500 v 1000 Describe what happens to the fish population for various initial populations. For 0 < P < 400, P(t) -Select--- For P 400, P(t)-Select-- For 400 < P < 600, P(t)-Select-- O Graph the solutions and compare with your sketches in part (b). P 500 (c) What are the equilibrium solutions? (Enter your answers as a comma-separated list.) Pa 1300 044 flip 0 50 100 150 200 250 300 350 P 1000 ***** .. 500 (d) Solve this differential equation explicitly, either by using partial fractions or with a computer algebra system. Use the initial populations 350 and 4 P-350 " P
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Plz solve all parts.
Transcribed Image Text:Let's modify the logistic differential equation of this example as follows:
P
of = 0.050 (1-1000)-
de
P =
(a) Suppose P(t) represents a fish population at time t, where t is measured in weeks. Explain the meaning of the final term in the equation (-12).
The term -12 represents a harvesting of fish at a constant rate-in this case, 12 [fish/week. This is the rate at which fish are caught.
(b) Draw a direction field for this differential equation. Use the direction field to sketch several solution curves.
P
P
1200) E
1000
●
800
600
P = 450
400
200
K 11
044
41
0 50 100 150 200 250 300 350
1200/
1000
12
800
600+
UTFALT
"
***LE
400
v
For 400 < P < 600, P(t)--Select---
For P600, P(t)-Select--
For P600, P(t) ---Select---
*****
v
v
1500
1000
Describe what happens to the fish population for various initial populations.
For 0 < P < 400, P(t)-Select-- v
For P = 400, P(t)-Select---
500
Graph the solutions and compare with your sketches in part (b).
P
(c) What are the equilibrium solutions? (Enter your answers as a comma-separated list.)
0
0
1300 1
1000
500
E
50 100 150 200 250 300 350
(d) Solve this differential equation explicitly, either by using partial fractions or with a computer algebra system. Use the initial populations 350 and 45
P = 350
U
P
Transcribed Image Text:Graph the solutions and compare with your sketches in part (b).
P
1500
1000
500
P
1500
1000
500-
t
50 100 150 200 250 300 350
50
t
100 150 200 250 300 350
O
P
1200아
1000
800
6000
O
400
2000
P
1200
1000
800
600
400
200
t
50 100 150 200 250 300 350
50
t
100 150 200 250 300 350
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